Question: When the height of a cylinder is doubled and its radius is increased by $200\%$, the cylinder's volume is multiplied by a factor of $X$. What is the value of $X$?
Explanation: The cylinder's original volume is $\pi r^2h$. The new height is $2h$ and the new radius is $r+\frac{200}{100}r=3r$. That means the new volume is $\pi (3r)^2(2h)=\pi r^2h(9)(2)$. The new volume is the original volume multiplied by a factor of $\boxed{18}$.